UNIVERSITY OF CAPE COAST
COLLEGE OF EDUCATION STUDIES
FACULTY OF SCIENCE AND TECHNOLOGY
EDUCATION
DEPARTMENT OF MATHEMATICS AND ICT
EDUCATION
EMA210: INTRODUCTORY STATISTICS II
GROUP ASSIGNMENT
GROUP 12
INDEX NUMBER
ET/MAT/20/0169
ET/MAT/20/0113
ET/MAT/20/0114
ET/MAT/20/0095
ET/MAT/21/0084
ET/MAT/20/0115
Question: Write on binomial distribution and provide three solved examples.
Binomial distribution
Binomial distribution formula for any random variable x, is given by
P(x:n,p)=
n
Cxpxqn-x; p-success, q-failure
𝑛!
n
Cx=
q=1-p, n-number of trials or occurrences
𝑥!(𝑛−𝑥)!
Example 1
A fair coin is tosses 6 times. Find the probability of obtaining exactly 4 heads.
Solution
S={H,T}
1
1
n(S)=2 P(H)=2
P(exactly 4 heads)=6
P(T)= 2 n=6 x=4
C (0.5) (0.5)
4
4
1
=
2
1
15(16)( 4)
15
=64
15
Therefore, the probability of obtaining exactly 4 heads when a coin is tossed 6 times is 64.
Example 2
One out of every bolts produced by a machine is defective. If 4 bolts are produced by the
machine at random, find the probability that exactly 2 are defective.
Solution
1
P(Defective)= 3
2
P(Non-defective)= 3
P( exactly 2 defective)= 4
C()()
2
=
1
1 2 2 2
3 3
4
6(9)( 9)
8
=27
8
Therefore, the probability of obtaining exactly 2 defective bolts when 4 bolts are produced is 27
Example 3
A fair coin is tossed 6 times. What is the probability of obtaining at least 5 heads?
Solution
S={H,T}
1
1
n(S)=2 P(H)=2
P( at least 5 heads)= 6
P(T)= 2
n=6 x= 5,6
C ( ) ( )+ C ( ) ( )
=
5
1 5 1
2 2
6
1
1
1
6
1 6 1 0
2 2
6(32)( 2)+(64)
6
1
=64+64
7
=64
7
Therefore, the probability of obtaining at least 5 heads when a coin is tossed 6 times is 64